Question: Rewrite as a simplified fraction. ${1.\overline{20} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 120.202...\\ 1x &= 1.202...\end{align*}}$ Subtracting the two equations, we have: ${99x = 119}$ ${x = \dfrac{119}{99}} \text{or} {1 \dfrac{20}{99}}$